A linearized Peaceman–Rachford splitting method for structured convex optimization with application to stable principal component pursuit

Abstract

Many applications arising from machine learning, statistics and image processing can be formulated as a convex minimization model with separable structures both in objective function and constraints. The Peaceman–Rachford splitting method is very efficient for solving these problems, but it is not convergent in the absence of some restrictive assumptions. In this paper, we propose a linearized Peaceman–Rachford splitting method by linearizing one subproblem. We analyze its convergence by proving the global convergence and establishing its worst-case convergence rate in the ergodic sense. Some randomly generated stable principal component pursuit problems are tested to illustrate the efficiency of the new algorithm.